Diagrams and schemes

Trees

What are the ‘categories’?

In the Categories, Aristotle identifies ten categories (in Latin ‘praedicamenta’) which can be used to describe everything in the world:

Substance (e.g. a man, the species man, the genus animal)

Quantity (e.g. line, number)

Relation (e.g. larger)

Quality (e.g. sweetness)

Doing (e.g. cooling)

Undergoing (e.g. being cooled)

Place (e.g. in the market square)

Time (e.g. yesterday)

Position (e.g. sitting)

Having (e.g having shoes on)

The first category, substance, describes what something is, what is its being (e.g. ‘Socrates is a man’; being a man is fundamental to the essence of what it is to be Socrates). The remaining categories are ‘accidents’, these are the properties of the substance, they describe how something is, properties which are not necessarily essential to what it is (e.g. ‘Socrates is sitting’; Socrates could equally be standing, but he would still be Socrates).

Porphyry, a third-century Greek philosopher, wrote an important work called the Isagoge, which was an introduction to Aristotle’s Categories. This work was later translated into Latin and commented upon by Boethius.

One of the important contributions of this work was a treatment of the first, and most important of Aristotle’s categories, substance. Porphyry investigated what substance consisted of by using *differentiae – looking at the essential features which distinguish one *species within a *genus from another. This process of distinguishing between genera was often visualised in medieval manuscripts in the form of a tree diagram.

* A genus (pl. genera) is a grouping of things sharing a particular characteristic (e.g. having substance). A genus can consist of sub-genera; in the case of substance, for example, things which are corporeal and things which are not corporeal etc., and ultimately these genera can be further divided into additional genera and, finally into species, (e.g. human) groupings, which are not genera for anything else and cannot be further divided.

* Differentiae are characteristics which distinguish one grouping of things from another. In philosophical terms they are ‘predicated’ of things.

[*make the definitions appear on click to avoid the slide being too wordy??]

Porphyry identifies five ‘predicables’, genus, species, differentiae, property and accident. This scheme shows what makes each predicable different from the others.

[I need to develop this slide and work out its relationship with the others]
[Link to manuscript description:

(p. 53) One of the earliest examples of a ‘Porphyrian tree’ – note that Plato, Cicero and Socrates are used as the examples of ‘homo’
(p. 52b) Insertion of a slip, giving the Isidorean definition of philosophy (Etymologiae II.24.3). This is written in the same hand as that which did the corrections throughout the manuscript. Places dialectic/logic within the broader context of the study of philosophy.
(p. 100) This is a fairly small manuscript (220mm x 165mm), suggesting that the scribe was economizing on parchment – here he has written around a large hole. Quotation marks are used to discern between text and commentary.
(p. 139) Scheme for syllogistic reasoning
(p. 164) Quotation marks are used to discern between text and commentary. Here a later user has added a small face in the margin and some pen trials/doodles (a, b, c etc)]

How can we use categories to reason about the world?
The ‘Porphyrian tree’ is a way to divide a category, genus, into its constituents, and in so doing work out what the sub-genera and species which make up this category consist of. It is a tool for thinking about what things are and working out what are the essential characteristics of particular species.
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[insert transcription as jpg image? Or overlay on to the image?]

Substance
- Corporeal [substance] / Incorporeal [substance]
- Animate [corporeal substance] / Inanimate [corporeal substance]
- Sensitive [animate corporeal substance] / Insensitive [animate corporeal substance]
- Rational [sensitive animate corporeal substance] / Irrational [sensitive animate corporeal substance
- Mortal [rational sensitive animate corporeal substance] / Immortal [rational sensitive animate corporeal substance]
- Socrates/Cicero/Plato [mortal rational sensitive animate corporeal substance]

At each point differentiae (e.g. ‘is it corporeal or not?’) are used to establish characteristics. Note – in this case the tree is worked out to a particular conclusion – to identify the characteristics of the human species. A human (with particular examples given here as Socrates, Plato, Cicero) is mortal, rational, sensitive, animate, corporeal and made of substance. But the scheme also identifies other genera which describe the living world. For example, a sensitive, animate, corporeal substance is, in other words, an animal, while an insensitive, animate, corporeal substance, is a plant.

It’s important to note that all of Aristotle’s categories could be expanded into ‘trees’ using the process of differentiation, but the category of substance was the one which was most commonly executed.

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The ‘Porphyrian tree’ was co-opted into different textual contexts. For example, in this example, a version of the Porphyrian tree is incorporated into a thirteenth-century manuscript of John of Damascus’ Logica (BnF lat. 16598, f. 37r). This manuscript was donated to the library at the Sorbonne by Gerard d’Abbeville [[[Abbeville.docx]]], a thirteenth-century master. Here, as might befit a book belonging to a theologian, Peter and Paul substitute for Plato and Socrates as examples of the species ‘man’.

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In this twelfth-century manuscript of Boethius’ commentary on the Topica of Cicero (Link to BnF lat. 7709, f. 52r – see form) a glossator has added a small schemes similar to a Porphyrian tree beside the discussion of species and genus in the text. The scheme, entitled ‘substantia’ (substance) gives the genera: substance, body animate, animal, man and ends with the example of Socrates. Here Porphyry’s tree is transported from its original textual context and used in an abbreviated form – presumably to help the reader recall the method of logical differentiation.

Why is it called a ‘tree’?
Depicting the process of differentiation as branching creates an image which looks like a tree, even though its root (in this case substance) is at its head! The similarity in form between the scheme and a tree was not lost on medieval scribes… In this manuscript, a copy of Decem categoriae, a text on the categories attributed in the medieval period to Augustine, a branching diagram similar to a Porphyrian tree has been added in the margin, complete with foliate details.
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Usia [substance, a Latin form of the Greek οὐσία]
Animal / Genus
Homo / Species
Cicero / Estheti [to feel?]

The tradition of referring to the ’Porphyrian tree’ as a tree can be traced back to the thirteenth century. The famous logical text book, Summulae logicales by Peter of Spain described ‘arbor Porphyriana’ and copies of the text were frequently illustrated with depictions of the Porphyrian tree as a tree – complete with leaves and branches. Like BnF lat. 16598, this manuscript was also part of the bequest of Gerard d’Abbeville to the library of the Sorbonne in the thirteenth century.
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Other ways of using schemes to think about the nature of being
The Porphyrian tree was just one example of how medieval scholars grappled with thinking about the nature of being.
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In these two copies of Martianus Capella’s De nuptiis… [link to Mariken] a small marginal diagram is appended to the section on dialectic. Circular in form, at its centre it has the word ‘homo’, ‘man’ then ‘animalitas’, ‘ratio’, ‘mortalitas’, ‘sensus’ – animality (i.e. being animate), reason, mortality and senstation – in the next circle. In the outermost circle we find the words ‘lapis’ (stone); ‘equus’ (horse); ‘arbor’ (tree) and ‘angelus’ (angel).

Starting in the centre and reading outwards one can conclude the following:
- that man differs from a stone as he is animate
- that man differs from a horse as he has reason
- that man differs from a tree as he can feel
- that man differs from an angel as he is mortal

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This scheme, inserted on a slip into a copy of the De decem categoriae also tackles the subject of substance (here termed oycia, a Latinised form of οὐσία and described as the ‘genus generalissimum’, the genus of all genera)
The left side of the scheme deals with the genus 'tree’, giving the example of a nut-bearing tree as a species of this genus. The right hand side of the scheme deals with the genus ‘stone’, giving the precious stone beryl as a species of this genus.
The central branch of the scheme deals with the the genus ‘animal’, with ‘man’ (here Cicero) the example of the species.
Animal, tree and stones are all types of substance but are each have different distinguishing qualities.

What was the impact of these various schemes of being on medieval dialectical discourse? I

• They permitted rational enquiry into the world – by establishing how everything which could be observed in the world fit into a particular genus, and by extension a particular species, qualified by various ‘accidents’, they provided a road map for describing and understanding the observed world
• But… what happens when you try to apply the categories to God, who was by definition (to a medieval thinker) reducible neither to the labels of substance or genus?
• Link to Mariken’s discussion of Eriugena

Honorius of Autun, Clavis physicae – a summary of Eriugena’s theory (BnF lat. 6734, f. 2r)

As well as using the device of the syllogism to describe the nature of God, the manuscript includes a scheme resembling the form of the Porphyrian tree and also using the technique of differentiation to establish what the qualities of God are.

Reading down the central line, we see He is the ‘principalis causa’, the ‘principal cause’, the ‘effectus causarum’, the ‘effective cause’, and the ‘finis omnium’, ‘the end of everything’. He is also ‘bonitas’, ‘goodness’ and ‘elementa’, ‘element’ (here in the sense of an ultimate substance)

The horizontal branches relate these qualities to his capacities (as expressed in the syllogistic statements at the top of the page – see Mariken), differentiating his qualities from other beings.

DRAFT: TO BE DEVELOPED

I want to add something in on discovering arguments through using the differentiae used by Boethius in De differentiis topicis – using BnF lat. 6400g LINK – which we can tie back into BPL 88 LINK as bawdiness in classroom. I have other examples for this too.